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All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

A Very High Order, Adaptable MESA Implementation for Aeroacoustic Computations

Since computational efficiency and wave resolution scale with accuracy, the ideal would be infinitely high accuracy for problems with widely varying wavelength scales. Currently, many of the computational aeroacoustics methods are limited to 4th order accurate Runge-Kutta methods in time which limits their resolution and efficiency. However, a new procedure for implementing the Modified Expansion Solution Approximation (MESA) schemes, based upon Hermitian divided differences, is presented which extends the effective accuracy of the MESA schemes to 57th order in space and time when using 128 bit floating point precision. This new approach has the advantages of reducing round-off error, being easy to program. and is more computationally efficient when compared to previous approaches. Its accuracy is limited only by the floating point hardware. The advantages of this new approach are demonstrated by solving the linearized Euler equations in an open bi-periodic domain. A 500th order MESA scheme can now be created in seconds, making these schemes ideally suited for the next generation of high performance 256-bit (double quadruple) or higher precision computers. This ease of creation makes it possible to adapt the algorithm to the mesh in time instead of its converse: this is ideal for resolving varying wavelength scales which occur in noise generation simulations. And finally, the sources of round-off error which effect the very high order methods are examined and remedies provided that effectively increase the accuracy of the MESA schemes while using current computer technology.

Dydson, Roger W.↗
NASA NTRS1987

Inelastic strain analogy for piecewise linear computation of creep residues in built-up structures

An analogy between inelastic strains caused by temperature and those caused by creep is presented in terms of isotropic elasticity. It is shown how the theoretical aspects can be blended with existing finite-element computer programs to exact a piecewise linear solution. The creep effect is determined by using the thermal stress computational approach, if appropriate alterations are made to the thermal expansion of the individual elements. The overall transient solution is achieved by consecutive piecewise linear iterations. The total residue caused by creep is obtained by accumulating creep residues for each iteration and then resubmitting the total residues for each element as an equivalent input. A typical creep law is tested for incremental time convergence. The results indicate that the approach is practical, with a valid indication of the extent of creep after approximately 20 hr of incremental time. The general analogy between body forces and inelastic strain gradients is discussed with respect to how an inelastic problem can be worked as an elastic problem.

Jenkins, Jerald M.↗
NASA NTRS1991

Basic research for the geodynamics program

The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.

Source record↗
NASA NTRS2020

Modeling and Control for a Flexible Inverted Pendulum Robot

This report describes the tasks accomplished during Fall 2020 at the Kennedy Space Center under the scope of the Robotic Control System Design internship project. These tasks primarily supported development of an augmented adaptive control system for an inverted pendulum (IP) robotic system on a 4-wheel mobile base (Penny). This system serves as an analogue to the control problems in the flight of rockets in the initial and latter stages of launch, and methods developed as part of this research can later be applied to more complex IP systems, such as launch vehicles. To more accurately model launch vehicles, a flexible aluminum pendulum is used both on the hardware and in the simulated models. In order to capture the flexible dynamics of the system, hardware modifications were made to Penny (including installation of a rate gyro at the tip of the pendulum). Simulink models were created to control and model the hardware system, and Simscape models were created/updated to model the system in simulation. MATLAB programs were created throughout the internship to analyze data generated from hardware and simulation runs. Linear fixed-gain controllers have been applied to the simulated and hardware system, and work continues with augmenting these controllers using sensor blending and direct output adaptive control methods to improve stabilization of system states and cancel flex dynamics. In addition to describing the work done to support these modeling efforts, an Independent Research and Technology Development (IR&TD) proposal for a lunar simulation with soil deformation modeling developed during the internship is briefly described.

Nashir A Janmohamed↗
NASA NTRS1995

The abundances of major elements in Cas A and Tycho supernova remnants

The objective of this program was to map the abundances of major elements such as O, Si, S, and Fe in the supernova remnants, Tycho and Cas A. The approach was based upon using archival cosmic X-ray data from several space missions, notably, the Einstein Observatory, EXOSAT, ROSAT, BBSRT, and ASCA. Two of the missions, Einstein and ROSAT, had high resolution telescopes that provided excellent images, but no spectral information. Two missions with much poorer resolution telescopes, BBXRT and ASCA, gave good spectral information through pulse height of signals in their cooled solid state detector, but rather crude spatial information. Our goal was to extract spectral information from the combined analysis of the Einstein and ROSAT images of Cas A and Tycho and to verify or refine the spectral map by checking its agreement with the BBSRT or ASCA spectra results for larger regions. In particular, we note that the Einstein and ROSAT telescopes have different spectral responses. The Einstein bandwidth includes the 2-4 keV region which is absent from ROSAT. Hence, by forming linear combinations of the Einstein and ROSAT images, we are able to resolve the contributions of the 0.5-2 keV band from the 2-4 keV band. The former contains lines of O and Fe while the latter is dominated by Si and S. We correct for the expansion that has taken place in the remnants during the ten-year interval between the Einstein and ROSAT measurements, but we must assume that no significant spectral changes have occurred during that time. The analysis of the Tycho SNR was completed and the results have been published. A copy of the paper is included. The analysis of Cas A has proved to be more complicated. It is continuing with support from another program. Part of the problem may be due to difficulties in the aspect information which is needed to precisely register the ROSAT and Einstein images.

Gorenstein, P.↗
NASA NTRS1994

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

Murthy, V. R.↗
NASA NTRS1993

An experimental study of the sources of fluctuating pressure loads beneath swept shock/boundary-layer interactions

An experimental research program providing basic knowledge and establishing a database on the fluctuating pressure loads produced on aerodynamic surfaces beneath three dimensional shock wave/boundary layer interactions is described. Such loads constitute a fundamental problem of critical concern to future supersonic and hypersonic flight vehicles. A turbulent boundary layer on a flat plate is subjected to interactions with swept planar shock waves generated by sharp fins at angle of attack. Fin angles from 10 to 20 deg at freestream Mach numbers of 3 and 4 produce a variety of interaction strengths from weak to very strong. Miniature Kulite pressure transducers flush-mounted in the flat plate are used to measure interaction-induced wall pressure fluctuations. The distributions of properties of the pressure fluctuations, such as their ring levels, amplitude distributions, and power spectra, are also determined. Measurements were made for the first time in the aft regions of these interactions, revealing fluctuating pressure levels as high as 160 dB. These fluctuations are dominated by low frequency (0-5 kHz) signals. The maximum ring levels in the interactions show an increasing trend with increasing interaction strength. On the other hand, the maximum ring levels in the forward portion of the interactions decrease linearly with increasing interaction sweep back. These ring pressure distributions and spectra are correlated with the features of the interaction flowfield. The unsteadiness of the off-surface flowfield is studied using a new, non-intrusive technique based on the shadow graph method. The results indicate that the entire lambda-shock structure generated by the interaction undergoes relatively low-frequency oscillations. Some regions where particularly strong fluctuations are generated were identified. Fluctuating pressure measurements are also made along the line of symmetry of an axisymmetric jet impinging upon a flat plate at an angle. This flow was chosen as a simple analog to the impinging jet region found in the rear portion of the shock wave/boundary layer interactions under study. It is found that a sharp peak in ring pressure level exists at or near the mean stagnation point. It is suggested that the phenomena responsible for this peak may be active in the swept interactions as well, and may cause the extremely high fluctuating pressures observed in the impinging jet region in the present experimental program.

Settles, G. S.↗
NASA NTRS2009

Massively Parallel Dantzig-Wolfe Decomposition Applied to Traffic Flow Scheduling

Optimal scheduling of air traffic over the entire National Airspace System is a computationally difficult task. To speed computation, Dantzig-Wolfe decomposition is applied to a known linear integer programming approach for assigning delays to flights. The optimization model is proven to have the block-angular structure necessary for Dantzig-Wolfe decomposition. The subproblems for this decomposition are solved in parallel via independent computation threads. Experimental evidence suggests that as the number of subproblems/threads increases (and their respective sizes decrease), the solution quality, convergence, and runtime improve. A demonstration of this is provided by using one flight per subproblem, which is the finest possible decomposition. This results in thousands of subproblems and associated computation threads. This massively parallel approach is compared to one with few threads and to standard (non-decomposed) approaches in terms of solution quality and runtime. Since this method generally provides a non-integral (relaxed) solution to the original optimization problem, two heuristics are developed to generate an integral solution. Dantzig-Wolfe followed by these heuristics can provide a near-optimal (sometimes optimal) solution to the original problem hundreds of times faster than standard (non-decomposed) approaches. In addition, when massive decomposition is employed, the solution is shown to be more likely integral, which obviates the need for an integerization step. These results indicate that nationwide, real-time, high fidelity, optimal traffic flow scheduling is achievable for (at least) 3 hour planning horizons.

Rios, Joseph Lucio↗
NASA NTRS1984

Air data position-error calibration using state reconstruction techniques

During the highly maneuverable aircraft technology (HiMAT) flight test program recently completed at NASA Ames Research Center's Dryden Flight Research Facility, numerous problems were experienced in airspeed calibration. This necessitated the use of state reconstruction techniques to arrive at a position-error calibration. For the HiMAT aircraft, most of the calibration effort was expended on flights in which the air data pressure transducers were not performing accurately. Following discovery of this problem, the air data transducers of both aircraft were wrapped in heater blankets to correct the problem. Additional calibration flights were performed, and from the resulting data a satisfactory position-error calibration was obtained. This calibration and data obtained before installation of the heater blankets were used to develop an alternate calibration method. The alternate approach took advantage of high-quality inertial data that was readily available. A linearized Kalman filter (LKF) was used to reconstruct the aircraft's wind-relative trajectory; the trajectory was then used to separate transducer measurement errors from the aircraft position error. This calibration method is accurate and inexpensive. The LKF technique has an inherent advantage of requiring that no flight maneuvers be specially designed for airspeed calibrations. It is of particular use when the measurements of the wind-relative quantities are suspected to have transducer-related errors.

Whitmore, S. A.↗
NASA NTRS1993

Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program (update to automatic flight trajectory design, performance prediction, and vehicle sizing for support of Shuttle and Shuttle derived vehicles) engineering manual

The Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program and its predecessors, the ROBOT and the RAGMOP programs, have had a long history of supporting MSFC in the simulation of space boosters for the purpose of performance evaluation. The ROBOT program was used in the simulation of the Saturn 1B and Saturn 5 vehicles in the 1960's and provided the first utilization of the minimum Hamiltonian (or min-H) methodology and the steepest ascent technique to solve the optimum trajectory problem. The advent of the Space Shuttle in the 1970's and its complex airplane design required a redesign of the trajectory simulation code since aerodynamic flight and controllability were required for proper simulation. The RAGMOP program was the first attempt to incorporate the complex equations of the Space Shuttle into an optimization tool by using an optimization method based on steepest ascent techniques (but without the min-H methodology). Development of the complex partial derivatives associated with the Space Shuttle configuration and using techniques from the RAGMOP program, the ROBOT program was redesigned to incorporate these additional complexities. This redesign created the MASTRE program, which was referred to as the Minimum Hamiltonian Ascent Shuttle TRajectory Evaluation program at that time. Unique to this program were first-stage (or booster) nonlinear aerodynamics, upper-stage linear aerodynamics, engine control via moment balance, liquid and solid thrust forces, variable liquid throttling to maintain constant acceleration limits, and a total upgrade of the equations used in the forward and backward integration segments of the program. This modification of the MASTRE code has been used to simulate the new space vehicles associated with the National Launch Systems (NLS). Although not as complicated as the Space Shuttle, the simulation and analysis of the NLS vehicles required additional modifications to the MASTRE program in the areas of providing additional flexibility in the use of the program, allowing additional optimization options, and providing special options for the NLS configuration.

Lyons, J. T.↗
NASA NTRS1996

Controlled Quantum Packets

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

DeMartino, Salvatore↗
NASA NTRS1996

Optimization Methodology for Unconventional Rocket Nozzle Design

Several current rocket engine concepts such as the bell-annular tripropellant engine, and the linear aerospike being proposed for the X-33, require unconventional three-dimensional rocket nozzles which must conform to rectangular or sector-shaped envelopes to meet integration constraints. These types of nozzles exist outside the current experience database, therefore, development of efficient design methods for these propulsion concepts is critical to the success of launch vehicle programs. Several approaches for optimizing rocket nozzles, including streamline tracing techniques, and the coupling of CFD analysis to optimization algorithms are described. The relative strengths and weaknesses of four classes of optimization algorithms are discussed: Gradient based methods, genetic algorithms, simplex methods, and surface response methods. Additionally, a streamline tracing technique, which provides a very computationally efficient means of defining a three-dimensional contour, is discussed. The performance of the various optimization methods on thrust optimization problems for tripropellant and aerospike concepts is assessed and recommendations are made for future development efforts.

Follett, W.↗
NASA NTRS1982

Computer program for post-flight evaluation of the control surface response for an attitude controlled missile

A FORTRAN IV coded computer program is presented for post-flight analysis of a missile's control surface response. It includes preprocessing of digitized telemetry data for time lags, biases, non-linear calibration changes and filtering. Measurements include autopilot attitude rate and displacement gyro output and four control surface deflections. Simple first order lags are assumed for the pitch, yaw and roll axes of control. Each actuator is also assumed to be represented by a first order lag. Mixing of pitch, yaw and roll commands to four control surfaces is assumed. A pseudo-inverse technique is used to obtain the pitch, yaw and roll components from the four measured deflections. This program has been used for over 10 years on the NASA/SCOUT launch vehicle for post-flight analysis and was helpful in detecting incipient actuator stall due to excessive hinge moments. The program is currently set up for a CDC CYBER 175 computer system. It requires 34K words of memory and contains 675 cards. A sample problem presented herein including the optional plotting requires eleven (11) seconds of central processor time.

Knauber, R. N.↗
NASA NTRS1993

Binary tree eigen solver in finite element analysis

This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling.

Akl, F. A.↗
NASA NTRS1989

A spatial operator algebra for manipulator modeling and control

A recently developed spatial operator algebra, useful for modeling, control, and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanizaton of specific algorithms is greatly simplified. The analytical formulation of the operator algebra, as well as its implementation in the Ada programming language are discussed.

Rodriguez, G.↗
NASA NTRS1972

Tests and analyses applicable to passenger ride quality of large transport aircraft

A test program was undertaken to determine airline passenger reaction to vibration environments that might be encountered in a supersonic transport or other large commercial jet aircraft. The principal problem addressed was to determine accelerations of vertical and lateral vibration that people find objectionable. Further questions experimentally posed were: (1) what is the relationship between human reactions to vertical and lateral vibration, (2) to single- and combined-frequency vibration, and (3) to single- and combined-axis vibration? Interest was confined to reactions to vibration in the frequency range of 0.20 to 7.0 Hz, a range typical of the vibration environment of a large airplane. Results indicated an increasing sensitivity to vertical vibration as frequency was increased from 1.0 to 7.0 Hz. Subjects were found most sensitive to lateral vibration in the 1.0 to 3.0 Hz range. There was a nearly linear decrease in sensitivity as frequency of lateral vibration was increased from 3.0 to 7.0 Hz.

Holloway, R. B.↗
NASA NTRS1981

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 4: Maintenance document (version 1.1)

The Maintenance Document is a guide to the PAN AIR software system, a system which computes the subsonic or supersonic linear potential flow about a body of nearly arbitrary shape, using a higher order panel method. The document describes the over-all system and each program module of the system. Sufficient detail is given for program maintenance, updating and modification. It is assumed that the reader is familiar with programming and CDC (Control Data Corporation) computer systems. The PAN AIR system was written in FORTRAN 4 language except for a few COMPASS language subroutines which exist in the PAN AIR library. Structured programming techniques were used to provide code documentation and maintainability. The operating systems accommodated are NOS 1.2, NOS/BE and SCOPE 2.1.3 on the CDC 6600, 7600 and Cyber 175 computing systems. The system is comprised of a data management system, a program library, an execution control module and nine separate FORTRAN technical modules. Each module calculates part of the posed PAN AIR problem. The data base manager is used to communicate between modules and within modules. The technical modules must be run in a prescribed fashion for each PAN AIR problem. In order to ease the problem of supplying the many JCL cards required to execute the modules, a separate module called MEC (Module Execution Control) was created to automatically supply most of the JCL cards. In addition to the MEC generated JCL, there is an additional set of user supplied JCL cards to initiate the JCL sequence stored on the system.

Baruah, P. K.↗
NASA NTRS1990

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 4: Maintenance document (version 3.0)

The Maintenance Document Version 3.0 is a guide to the PAN AIR software system, a system which computes the subsonic or supersonic linear potential flow about a body of nearly arbitrary shape, using a higher order panel method. The document describes the overall system and each program module of the system. Sufficient detail is given for program maintenance, updating, and modification. It is assumed that the reader is familiar with programming and CRAY computer systems. The PAN AIR system was written in FORTRAN 4 language except for a few CAL language subroutines which exist in the PAN AIR library. Structured programming techniques were used to provide code documentation and maintainability. The operating systems accommodated are COS 1.11, COS 1.12, COS 1.13, and COS 1.14 on the CRAY 1S, 1M, and X-MP computing systems. The system is comprised of a data base management system, a program library, an execution control module, and nine separate FORTRAN technical modules. Each module calculates part of the posed PAN AIR problem. The data base manager is used to communicate between modules and within modules. The technical modules must be run in a prescribed fashion for each PAN AIR problem. In order to ease the problem of supplying the many JCL cards required to execute the modules, a set of CRAY procedures (PAPROCS) was created to automatically supply most of the JCL cards. Most of this document has not changed for Version 3.0. It now, however, strictly applies only to PAN AIR version 3.0. The major changes are: (1) additional sections covering the new FDP module (which calculates streamlines and offbody points); (2) a complete rewrite of the section on the MAG module; and (3) strict applicability to CRAY computing systems.

Purdon, David J.↗